A function ψ(x,y,z) appearing in Schrödinger's equation in wave mechanics. The wave function is a mathematical expression involving the coordinates of a particle in space. If the Schrödinger equation can be solved for a particle in a given system (e.g. an electron in an atom) then, depending on the boundary conditions, the solution is a set of allowed wave functions (eigenfunctions) of the particle, each corresponding to an allowed energy level (eigenvalue). The physical significance of the wave function is that the square of its absolute value, |ψ|2, at a point is proportional to the probability of finding the particle in a small element of volume, dxdydz, at that point. For an electron in an atom, this gives rise to the idea of atomic and molecular orbitals.